A022234 Gaussian binomial coefficients [ n,5 ] for q = 7.

1, 19608, 336416907, 5670690600800, 95347005938577702, 1602592475815614015216, 26935000671139346639437914, 452697105941691435357049202400, 7608481579300344488889504665693103, 127875753071992714335358328311551866824

Offset

5,2

References

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

Links

Vincenzo Librandi, Table of n, a(n) for n = 5..200

Formula

a(n) = Product_{i=1..5} (7^(n-i+1)-1)/(7^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

G.f.: x^5/((1 - x)*(1 - 7*x)*(1 - 49*x)*(1 - 343*x)*(1 - 2401*x)*(1 - 16807*x)). - Ilya Gutkovskiy, Aug 06 2016

Mathematica

Table[QBinomial[n, 5, 7], {n, 5, 20}] (* Vincenzo Librandi, Aug 06 2016 *)

Prog

(Sage) [gaussian_binomial(n, 5, 7) for n in range(5, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=5; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016
(PARI) r=5; q=7; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 13 2018

Crossrefs

Sequence in context: A156721 A174760 A115472 * A082890 A109569 A204665

Adjacent sequences: A022231 A022232 A022233 * A022235 A022236 A022237

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 06 2016

Status

approved